Simplify to lowest terms. $\dfrac{100}{70}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 100 and 70? $100 = 2\cdot2\cdot5\cdot5$ $70 = 2\cdot5\cdot7$ $\mbox{GCD}(100, 70) = 2\cdot5 = 10$ $\dfrac{100}{70} = \dfrac{10 \cdot 10}{ 7\cdot 10}$ $\hphantom{\dfrac{100}{70}} = \dfrac{10}{7} \cdot \dfrac{10}{10}$ $\hphantom{\dfrac{100}{70}} = \dfrac{10}{7} \cdot 1$ $\hphantom{\dfrac{100}{70}} = \dfrac{10}{7}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{100}{70}= \dfrac{2\cdot50}{2\cdot35}= \dfrac{2\cdot 5\cdot10}{2\cdot 5\cdot7}= \dfrac{10}{7}$